Abstract
When electrons are driven through unconventional magnetic structures, such as skyrmions, they experience emergent electromagnetic fields that originate several Hall effects. Independently, ground-state emergent magnetic fields can also lead to orbital magnetism, even without the spin–orbit interaction. The close parallel between the geometric theories of the Hall effects and of the orbital magnetization raises the question: does a skyrmion display topological orbital magnetism? Here we first address the smallest systems with nonvanishing emergent magnetic field, trimers, characterizing the orbital magnetic properties from first-principles. Armed with this understanding, we study the orbital magnetism of skyrmions and demonstrate that the contribution driven by the emergent magnetic field is topological. This means that the topological contribution to the orbital moment does not change under continuous deformations of the magnetic structure. Furthermore, we use it to propose a new experimental protocol for the identification of topological magnetic structures, by soft X-ray spectroscopy.
Highlights
The magnetic moment has two contributions: the spin magnetic moment and the orbital magnetic moment, which are due to lifting of spin and orbital degeneracy, respectively
The topology can be ascertained via full knowledge of the three-dimensional magnetic structure, which can be mapped via small-angle neutron scattering[14], Lorentz force microscopy[15], scanning tunnelling microscopy[20] and soft X-ray magnetic circular dichroism az b c d
We exploit the distinct properties of the chirality- and spin–orbit coupling (SOC)-driven orbital moments to propose a new experimental protocol, based on XMCD, that can directly establish whether a given sample has a topological magnetic structure
Summary
The magnetic moment has two contributions: the spin magnetic moment and the orbital magnetic moment, which are due to lifting of spin and orbital degeneracy, respectively. Ground states hosting bound currents require lifting of orbital degeneracy Such ground-state currents have been proposed for magnetic structures where the magnetic moments do not all lie in the same plane, that is, with nonvanishing scalar spin chirality, C123 1⁄4 S1 Á (S2 Â S3)a0 (refs 1–3). We consider three aspects of the chirality-driven orbital moment physics We characterize their properties using symmetry and the underlying electronic structure, clearly separating the SOC-driven from the chirality-driven orbital moments, by performing first-principles calculations for magnetic trimers. We exploit the distinct properties of the chirality- and SOC-driven orbital moments to propose a new experimental protocol, based on XMCD, that can directly establish whether a given sample has a topological magnetic structure
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